First: It is possible the outside TV is fried.. Generators can do strange things when they shut down under load.. (like voltage spikes) That said there are other suspects I'd go after first.
GFCI: Since power is being consumed OUTSIDE, the outlet it's coming from may be GFCI protected.. Should be in fact.. And said GFCI (not necessarly the actual outlet but one to which it is daisy chained) may have tripped.
Circuit breakers.. Both in your breaker panel indoors AND on the generator.
Transfer switch.
SCREW LOOSE.. Many RVers have a few screws loose.. One of the circuit breakers in this rig took a full two turns and then some before I even felt resistance,, That was NOT the worst (The worst was a neighbor, in one of the CG's I stay at.. Of the six screws inside his Marinco outlet (The part of the power cord that connects to the inlet on the side of your RV) all six were loose... L-1, L-2, Neutral, Safety ground and 2 cable clamp screws. Outlet fell right off the cord)
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times